Subtracting complex numbers

we're asked to subtract and we have the complex number 2 minus 3i and from that we are subtracting 6 minus 18i so the first thing I'd like to do here is to just kind of get rid of these parentheses so we just have a bunch of real parts and imaginary parts that we can then add up together so we have 2 minus 3i and then we're subtracting this entire quantity and to get rid of the parentheses we can just distribute the negative sign or another way to think about it we can say that this is negative 1 times all of this so we can just distribute the negative sign a negative 1 times 6 is negative 6 let me do these in magenta so this is negative 6 and the negative 1 times negative 18i well that's just going to be positive positive 89 egative times a negative is a positive and now we want to add the real parts and we want to add the imaginary parts so here's a real part here 2 and then we have a minus 6 so we have 2 minus 6 and we want to add the imaginary parts we have a negative let me do that in a different color we have a negative 3i right over here so negative 3i or minus 3i right over there and then we have a plus 18 I or positive 18 I so then we have a positive 18 I if you add the real parts 2 minus 6 is negative 4 and you imagine add the add the imaginary parts if I have negative 3 of something and to that I add 18 of something well that's just going to leave me with 15 of that something or another way you could think about if I have 18 of something and I subtract 3 of that something I'll have 15 of that something and in this case the something is the ahmet is i is the imaginary unit so this is so this is going to be plus 15 plus 15 i and we are done